Question

A ball of radius R carries a positive charge whose volume density depends only on a separation r from the ball’s centre as $\rho ={\rho }_0(1-\frac{r}{R})$, where ${\rho }_0$ is a constant. Assuming the permittivities of the ball and the environment to be equal to unity, find the ratio of the magnitude of the electric field strength inside the sphere to that of the outside.

• A. $\frac{1}{R^3}(r-\frac{3r^2}{4R})$
• B. $\frac{1}{R^3}(r^3-\frac{3r^4}{4R})$
• C. $\frac{4}{R^3}(r^3-\frac{3r^4}{4R})$
• D. 1

Answer 1

The correct option is C $\frac{4}{R^3}(r^3-\frac{3r^4}{4R})$